where dE/dt is the rate of change of the internal energy E of the detector with a certain relation between the energy and the temperature T (for example E ~ T^2, page 64), Output is the (net) outgoing radiance from the detector and Input is the (net) incoming radiance from the object. The detector at lower temperature than the object reacts by heating up until in radiative equilibrium with dE/dt = 0 and Output = Input, it assumes the same temperature as the object. The detector thus records an increase in temperature from its known instrument background temperature and can thus report the temperature of the object, by remote infrared thermal sensing based on radiative equilibrium.

To measure radiance, would require measuring the dynamic response of the detector by reading dE/dt and then reconstructing Input from dE/dt, E and Output, which is much more difficult. Remote infrared sensing involving a sensor of the form described (e.g. thermopile), reports temperature. Radiance is then constructed from temperature using some guess work and calibration. In the absence of true direct measurements of radiance, this construction has come to define radiance in a circular way.

To record a lower temperature than the instrument background temperature is also difficult since it requires effective shielding of the detector.

PS2 There is a connection to the option market with the value of an option constructed by the Black-Scholes formula, which has created an artificial fictional market leading to the present crisis in the world economy. Replace Black-Scholes with an artificial incorrect version of Planck, and you have climate alarmism adding to the crisis.

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Take a bolometer for instance. It works by connecting the absorbing part of the detector with a heat sink that is held at a low temperature, it is more than safe to ignore any losses from the detector.

For a bolometer the correct equation read

C*d(DT)/dt + G*DT = P,

C is the heat capacity of the receiving part of the detector, G is the conductance to a heat sink at temperature T0, P is the absorbed incoming power and DT is the temperature difference between the absorbing part and the heat sink.

In steady state

DT = P/G

which is a good starting point if you want to analyze the performance further. You have a direct relation between absorbed power and temperature difference.

This is a trivial model that can model anything, which no commercial company could dare to try to sell. It is like modeling the world with straight line through the origin and claim thatthe slope can be determined by calibration.

You measure the applied amount of electric energy that is needed to heat a resistor (you heat it with a DC current) so that it's resistance matches the resistance that is caused by the increased temperature in the bolometer. This increasing temperature is the result of applied power to the bolometer.

As as you measure DT at stationary state, it is temperature you are measuring, and connecting radiance to temperature requires emmisivity which is unknown in general. To guess radiance from temperature is guess work.

It needs to be explained why one cannot simply identify the term C*d(DT)/dt as dE/dt, and G*DT as output from the detector while it comes to temperature balance with the object--thus making the two equations under discussion the same.

If the aim is to measure temperature, no model is needed, since the temperature is what is registered. If the aim is to measure radiance then a model is needed, and then my model as a wave model with small damping is much better than the trivial model suggested which can model anything. But as said measuring radiance is more difficult.

You can only measure temperature, or net heat transfer, but not gross input because you don't know the net output. Gross input/output are fictional quantities connected to an incorrect reading of Planck's radiation law as expressing two-way heat transfer, while the correct reading is one-way from warm to cold as net heat transfer.

This is the same discussion as an earlier one about heating chickens in microwave ovens, see e g

http://claesjohnson.blogspot.se/2011/07/sky-dragon-strikes-back.html

The chicken will in stationary state assume the temperature of blackbody with the radiance of the input. By checking the state of the chicken you can determine that temperature. If the input temp is too low the chicken will stay raw.